InterviewSolution
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InterviewSolution
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A particle at the end of a spring executes S.H,M with a period `t_(2)` If the period of oscillation with two spring in .A. `T = t_(1) +t_(2)`B. `T^(2) =t_(1)^(2) +t_(2)^(2)`C. `T^(-1) =t_(2)^(-1) +t_(2)^(-1)`D. `T^(-2)=t_(1)^(-2)+t_(2)^(-2)` |
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Answer» Correct Answer - B Time period of spring `T = 2pi sqrt(((m)/(k)))` `k` being the force constant of spring. For first spring. `t_(1) = 2pi sqrt(((m)/(k_(1)))) ….(1)` For second spring `t_(2) = 2pi sqrt(((m)/(k_(2)))) …(2)` The effective force constant in their series combination is `k = (k_(1)k_(2))/(k_(1)+k_(2))`. Therefore, time period of combination `T = 2pi sqrt([(m(k_(1)+k_(2)))/(k_(1)k_(2))])` `rArr T^(2) = (4pi^(2)m(k_(1)+k_(2)))/(k_(1)k_(2)) ....(3)` From equations (1) and (2), we obtain `t_(1)^(2) +t_(2)^(2) =4pi^(2) ((m)/(k_(1))+(m)/(k_(2))) :. t_(1)^(2) +t_(2)^(2) =T^(2)` [from eq (3)] |
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